This invention in general relates to interferometers, e.g., displacement measuring and dispersion interferometers that measure displacements of a measurement object such as a mask stage or a wafer stage in a lithography scanner or stepper system, and also interferometers that monitor wavelength and determine intrinsic properties of gases. More particularly, it relates to optical means by which cyclic errors that would otherwise be present in the signals generated in such interferometers can be acceptably reduced or substantially eliminated.
Displacement measuring interferometers monitor changes in the position and orientation of a measurement object relative to a reference object based on an optical interference signal. The interferometer generates the optical interference signal by overlapping and interfering a measurement beam reflected from the measurement object with a reference beam reflected from the reference object.
In many applications, the measurement and reference beams have orthogonal polarizations and different frequencies. The different frequencies can be produced, for example, by laser Zeeman splitting, acousto-optical modulation, or internal to the laser using birefringent elements, or the like. The orthogonal polarizations allow a polarizing beam splitter to direct the measurement and reference beams to the measurement and reference objects, respectively, and combine the reflected measurement and reference beams to form overlapping exit measurement and reference beams. The overlapping exit beams form an output beam that subsequently passes through a polarizer. The polarizer mixes polarizations of the exit measurement and reference beams to form a mixed optical beam. Components of the exit measurement and reference beams in the mixed optical beam interfere with one another so that the intensity of the mixed beam varies with the relative phase of the exit measurement and reference beams. A detector measures the time-dependent intensity of the mixed beam and generates an electrical interference signal proportional to that intensity. When the measurement and reference beams have different frequencies, the electrical interference signal includes a xe2x80x9cheterodynexe2x80x9d signal having a beat frequency equal to the difference between the frequencies of the exit measurement and reference beams. If the lengths of the measurement and reference paths are changing relative to one another, e.g., by translating a stage that includes the measurement object, the measured beat frequency includes a Doppler shift equal to 2xcexdnpL/xcex, where xcexd is the relative speed of the measurement and reference objects, xcex is the wavelength of the measurement and reference beams, n is the refractive index of the medium through which the light beams travel, e.g., air or vacuum, and p is the number of passes to the reference and measurement objects. Changes in the relative position of the measurement object correspond to changes in the phase of the measured interference signal, with a 2xcfx80 phase change substantially equal to a distance change L of xcex/(np), where L is a round-trip distance change, e.g., the change in distance to and from a stage that includes the measurement object.
Unfortunately, this equality is not always exact. Many interferometers include nonlinearities such as those known as xe2x80x9ccyclic errors.xe2x80x9d The cyclic errors can be expressed as contributions to the phase and/or the intensity of the measured interference signal and have a sinusoidal dependence on the change in optical path length pnkL. In particular, the first order cyclic error in phase has a sinusoidal dependence on (2xcfx80pnL)/xcex and the second order cyclic error in phase has a sinusoidal dependence on (2xcfx80pnL)/xcex. Higher order cyclic errors can also be present.
Cyclic errors can be produced by xe2x80x9cbeam mixing,xe2x80x9d in which a portion of an input beam that nominally forms the reference beam propagates along the measurement path and/or a portion of an input beam that nominally forms the measurement beam propagates along the reference path. Such beam mixing can be caused by ellipticity in the polarizations of the input beams and imperfections in the interferometer components, e.g., imperfections in a polarizing beam splitter used to direct orthogonally polarized input beams along respective reference and measurement paths. Because of beam mixing and the resulting cyclic errors, there is not a strictly linear relation between changes in the phase of the measured interference signal and the relative optical path length, pnL, between the reference and measurement paths. If not compensated, eliminated or acceptably reduced, cyclic errors caused by beam mixing can limit the accuracy of distance changes measured by an interferometer. Cyclic errors can also be produced by imperfections in transmissive surfaces that produce undesired multiple reflections within the interferometer and imperfections in components such as retroreflectors and/or phase retardation plates that produce undesired ellipticities in beams in the interferometer. For a general reference on the theoretical cause of cyclic error, see, for example, C. W. Wu and R. D. Deslattes, xe2x80x9cAnalytical modelling of the periodic nonlinearity in heterodyne interferometry,xe2x80x9d Applied Optics, 37, 6696-6700, 1998.
In dispersion measuring applications, optical path length measurements are made at multiple wavelengths, e.g., 532 nm and 1064 nm, and are used to measure dispersion of a gas in the measurement path of the distance measuring interferometer. The dispersion measurement can be used to convert the optical path length measured by a distance measuring interferometer into a physical length. Such a conversion can be important since changes in the measured optical path length can be caused by gas turbulence and/or by a change in the average density of the gas in the measurement arm even though the physical distance to the measurement object is unchanged. In addition to the extrinsic dispersion measurement, the conversion of the optical path length to a physical length requires knowledge of an intrinsic value of the gas. The factor xcex93 is a suitable intrinsic value and is the reciprocal dispersive power of the gas for the wavelengths used in the dispersion interferometry. The factor xcex93 can be measured separately or based on literature values. Cyclic errors in the interferometer also contribute to dispersion measurements and measurements of the factor xcex93. In addition, cyclic errors can degrade interferometric measurements used to measure and/or monitor the wavelength of a beam.
Systems and methods have been provided for identifying, quantifying and compensating for cyclic errors as, for example, those described in U.S. Pat. No. 6,246,481 issued on Jun. 12, 2001 in the name of Henry A. Hill for xe2x80x9cSYSTEMS AND METHODS FOR QUANTIFYING NONLINEARITIES IN INTERFEROMETRY SYSTEMS.xe2x80x9d Such systems and methods rely on the implementation of various algorithms via high speed electronics to operate.
Accordingly, it is a primary object of the present invention to provide a simple optical solution for substantially eliminating and/or reducing cyclic errors in interferometer systems.
It is another object of the present invention to provide an optical solution to the elimination and/or reduction of cyclic errors in interferometer systems to relieve the burden that would otherwise be placed on associated electronics.
It is still another object of the present invention to provide an optical solution to the elimination and/or reduction of cyclic errors to reduce the accuracy or requirements imposed on the various components of interferometry systems.
Other objects of the invention will, in part, be obvious and will, in part, appear hereinafter when the description to follow is read in conjunction with the drawings.
The invention comprises methods and apparatus for reducing subharmonic cyclic errors by rotating by a small angle an interferometer or elements thereof. The rotation of the interferometer or selective elements thereof introduces a corresponding small angle between a subharmonic type spurious beam that subsequently interferes with either the reference or measurement beam so that the fringe contrast of the interference terms between the subharmonic spurious beam and either the reference or measurement beam is reduced by a required factor for a given use application thereby reducing nonlinearities in the phase signal. A subharmonic type spurious beam is one that results in a subharmonic cyclic error if not otherwise compensated or eliminated.